The latest updates to that page (as of Sept. 19, 2012) state (emphasis added):

Java SE 6 End of Public Updates Notice

After February 2013, Oracle will no longer post updates of Java SE 6 to
its public download sites. Existing Java SE 6 downloads already posted
as of February 2013 will remain accessible in the Java Archive
on Oracle Technology Network. Developers and end-users are encouraged
to update to more recent Java SE versions that remain available for
public download. For enterprise customers, who need continued access to
critical bug fixes and security fixes as well as general maintenance for
Java SE 6 or older versions, long term support is available through Oracle Java SE Support .

What does this mean for Oracle E-Business Suite users?

EBS users fall under the category of "enterprise users" above.
Java is an integral part of the Oracle E-Business Suite technology
stack, so EBS users will continue to receive Java SE 6 updates from
February 2013 to the end of Java SE 6 Extended Support in June 2017.

In other words, nothing will change for EBS users after February 2013.

EBS users will continue to receive critical bug fixes and security fixes as well as general maintenance for Java SE 6. These Java SE 6 updates will be made available to EBS users for the Extended Support periods documented in the Oracle Lifetime Support policy document for Oracle Applications (PDF):

EBS 11i Extended Support ends November 2013

EBS 12.0 Extended Support ends January 2015

EBS 12.1 Extended Support ends December 2018

How can EBS customers obtain Java 6 updates after the public end-of-life?

Will EBS users be forced to upgrade to JRE 7 for Windows desktop clients?

No. This upgrade will be highly recommended but currently remains optional. JRE 6 will be available to Windows users to run with EBS for
the duration of your respective EBS Extended Support period. Updates will be delivered via My Oracle Support, where you can continue to receive critical bug fixes and security fixes as well as general maintenance for JRE 6 desktop clients.

The certification of Oracle E-Business Suite with JRE 7 (for desktop
clients accessing EBS Forms-based content) is in its final stages. If
you plan to upgrade your EBS desktop clients to JRE 7 when that
certification is released, you can get a head-start on that today.

Coexistence of JRE 6 and JRE 7 on Windows desktops

The upgrade to JRE 7 will be highly recommended for EBS users, but some users may need to run both JRE 6 and 7 on their Windows desktops
for reasons unrelated to the E-Business Suite.

Most EBS configurations
with IE and Firefox use non-static versioning by default. JRE 7 will
be invoked instead of JRE 6 if both are installed on a Windows desktop.
For more details, see "Appendix B: Static vs. Non-static Versioning and
Set Up Options" in Notes 290801.1 and 393931.1.

Auto-update will only keep JRE 7 up-to-date for Windows users with both JRE 6 and 7 installed.

JRE 6 users are strongly encouraged to apply the latest Critical Patch Updates as soon as possible after each release. The Jave SE CPUs will be available via My Oracle Support. EBS users can find more information about JRE 6 and 7 updates here:

Will EBS users be forced to upgrade to JDK 7 for EBS application tier servers?

No. This upgrade will be highly recommended but will be optional for EBS application tier servers running on Windows, Linux, and Solaris. You can
choose to remain on JDK 6 for
the duration of your respective EBS Extended Support period. If you
remain on JDK 6, you will continue to receive critical bug fixes and
security fixes as well as general maintenance for JDK 6.

The certification of Oracle E-Business Suite with JDK 7 for EBS application tier servers on Windows, Linux, and Solaris as well as other platforms such as IBM AIX and HP-UX is planned. Customers running platforms other than Windows, Linux, and Solaris should refer to their Java vendors's sites for more information about their support policies.